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S_A_V [24]
3 years ago
9

Solve each equation (Isolating first)

Mathematics
2 answers:
Dvinal [7]3 years ago
7 0

3 \times {( \frac{1}{8} )}^{2x}  = 12 \\ \Leftrightarrow {( \frac{1}{8} )}^{2x}  = 4 \\ \Leftrightarrow  {( {2}^{ - 3}) }^{2x}  =  {2}^{2}  \\ \Leftrightarrow  {2}^{ - 6x}  =  {2}^{2}  \\ \Leftrightarrow  - 6x = 2 \\ \Leftrightarrow x =  -  \frac{1}{3}  \\  \\ 2 {\sqrt[3]{5}}^{4x}  = 50 \\ \Leftrightarrow  { \sqrt[3]{5} }^{4x}  = 25 \\ \Leftrightarrow  {5}^{ \frac{4x}{3} }  =  {5}^{2}  \\ \Leftrightarrow  \frac{4x}{3}  = 2 \\ \Leftrightarrow 4x = 6 \\ \Leftrightarrow x =  \frac{3}{2}

Sedaia [141]3 years ago
3 0

Answer to Q1:

x= -1/3

Step-by-step explanation:

We have given the equations.

We have to solve these equations.

The first equation is :

3.(\frac{1}{8})^{2x}

(\frac{1}{8})^{2x}=4

(2^{-3x})^{2x}=4

2^{-6x}=4

2^{-6x}=2^{2}

As we know that bases are same then exponents are equal.

-6x = 2

x = 2/-6

x=-1/3

Answer to Q2:

x = 3/2

Step-by-step explanation:

The given equation is :

2.\sqrt[3]{5}^{4x}=50

We have to find the value of x.

First,we multiply both sides of equation by 1/2 we get,

5^{4x/3}=25

5^{4x/3}=5^{2}

4x/3=2

4x = 6

x = 3/2

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3 years ago
a culture started with 2000 bacteria. after 6 hours it grew to 2400 bacteria. predict how many bacteria will be present after 16
valentina_108 [34]
Hi!

Let's find how much bacteria it grows per hour. 
2400 - 2000 = 400
bacteria per (divided by) hour
400/6 = 66.7
After 16 hours...
66.7 x 16 = 1067.2
Plus the original amount of bacteria
1067.2 + 2400 = 3467.2

The answer is 3067.2

Hope this helps! :)
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8 0
3 years ago
Solve for y<br> 20x + 5y = 30<br> y = 0<br> simplify
stepladder [879]
It should be 25xy that is the correct answer i did this today
5 0
3 years ago
Read 2 more answers
The equation y = \large 1\frac{1}{2}x represents the number of cups of dried fruit, y, needed to make x pounds of granola. Deter
Natasha2012 [34]

Answer:

(1\frac{1}{2},1) - False

(4,6) - True

(18,12) -- False

(0,0) -- True

(2\frac{1}{2},3\frac{3}{4}) -- True

Step-by-step explanation:

The points are

(1\frac{1}{2},1) , (4,6), (18,12), (0,0) and (2\frac{1}{2},3\frac{3}{4}) ---- missing from the question

Given

y = 1\frac{1}{2}x

Required

Determine if each of the points would be on y = 1\frac{1}{2}x

To do this, we simply substitute the value of x and of each point in y = 1\frac{1}{2}x.

(a) (1\frac{1}{2},1)

In this case;

x = 1\frac{1}{2} and y = 1

y = 1\frac{1}{2}x becomes

y = 1\frac{1}{2} * 1\frac{1}{2}

y = \frac{3}{2} * \frac{3}{2}

y = \frac{9}{4}

y = 2\frac{1}{4}

<em>The point </em>(1\frac{1}{2},1)<em>  won't be on the graph because the corresponding value of y for </em>x = 1\frac{1}{2}<em> is </em>y = 2\frac{1}{4}<em></em>

(b) (4,6)

In this case;

x = 4

y = 6

y = 1\frac{1}{2}x becomes

y = 1\frac{1}{2} * 4

y = \frac{3}{2} * 4

y = \frac{3* 4}{2}

y = \frac{12}{2}

y = 6

<em>The point </em>(4,6)<em>  would be on the graph because the corresponding value of y for </em>x = 4 is y = 6

(c) (18,12)

In this case:

x = 18;y = 12

y = 1\frac{1}{2}x becomes

y = 1\frac{1}{2} * 18

y = \frac{3}{2} * 18

y = \frac{3* 18}{2}

y = \frac{54}{2}

y = 27

<em>The point </em>(18,12)<em>  wouldn't be on the graph because the corresponding value of y for </em>x = 18<em> is </em>y = 12<em></em>

(d) (0,0)

In this case;

x =0; y = 0

y = 1\frac{1}{2}x becomes

y = 1\frac{1}{2} * 0

y = 0

<em>The point </em>(0,0)<em>  would be on the graph because the corresponding value of y for </em>x = 0 is y = 0

(e) (2\frac{1}{2},3\frac{3}{4})

In this case:

x = 2\frac{1}{2}; y = 3\frac{3}{4}

y = 1\frac{1}{2}x becomes

y = 1\frac{1}{2} * 2\frac{1}{2}

y = \frac{3}{2} * \frac{5}{2}

y = \frac{15}{4}

y = 3\frac{3}{4}

<em>The point </em>(2\frac{1}{2},3\frac{3}{4}) <em>  would be on the graph because the corresponding value of y for </em>x = 2\frac{1}{2} is y = 3\frac{3}{4}

3 0
3 years ago
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
insens350 [35]

(2y² + 7y + 11) - (8y² - 5y + 7) you can distribute the negative sign to the second expression and then combine the like terms

new expression: (2y² + 7y + 11) (-8y² + 5y - 7)

2y² and -8y² equals -6y²

7y and 5y equals 12y

11 and -7 equals 4

The answer is -6y² + 12y + 4

5 0
3 years ago
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